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Градиентный бустинг. Реализация с нуля на Python и разбор особенностей его модификаций (XGBoost, CatBoost, LightGBM)

На сегодняшний день градиентный бустинг (gradient boosting machine) является одним из основных production-решений при работе с табличными, неоднородными данными, поскольку обладает высокой производительностью и точностью, а если быть точнее, то его модификации, речь о которых пойдёт чуть позже.

В данной статье представлена не только реализация градиентного бустинга GBM с нуля на Python, но а также довольно подробно описаны ключевые особенности его наиболее популярных модификаций.

Ноутбук с данными алгоритмами можно загрузить на Kaggle (eng) и GitHub (rus).

Содержание

Gradient Boosting Machine

Gradient Boosting Machine

Как и в случае с Adaboost, градиентный бустинг добавляет базовые модели в ансамбль последовательно, однако вместо обучения моделей с учётом весов на основе ошибок предшественников, в данном случае модели обучаются на остаточных ошибках (residual errors), допущенных предыдущими моделями.

Принцип работы градиентного бустинга для регрессии

Алгоритм строится следующим образом:

1) первоначальному прогнозу присваивается среднее значение y_train для всех образцов;
2) рассчитываются остатки модели на основе антиградиента функции потерь;
3) регрессионное дерево обучается на X_train и остатках, далее делается прогноз на X_train;
4) полученный прогноз добавляется к первоначальному и шаги 2-4 повторяются для каждого дерева;
5) после обучения всех моделей снова создаётся первоначальный прогноз из шага 1;
6) далее делаются прогнозы для X_test на обученных деревьях и добавляются к первоначальному;
7) полученная сумма и будет конечным прогнозом.

Формулы для расчётов

Функция потерь: $L(y_i, F(x_i)) = \frac{1}{2} (y_i - F(x_i))^2$

Остатки: $r_{ik} = -\left[\frac{\partial L(y_i, F(x_i))}{\partial F(x_i)}\right]_ {F(x) = F_{m-1}(x)} = y_{i} - F_{m-1}(x_i)$

Принцип работы градиентного бустинга для классификации

В случае классификации дела обстоят немного сложнее: к каждому уникальному классу необходимо применить one-hot encoding и перевести в вероятности с помощью softmax-функции, а к прогнозам деревьев добавить коэффициент $\gamma$ , который регулирует степень вклада каждого нового дерева в общую модель для снижения переобучения. Также качество прогнозов градиентного бустинга можно существенно улучшить, применив концепцию K-class LogitBoost: для каждого дерева рассчитываются веса, а только потом на их основе остатки.

Алгоритм строится следующим образом:

1) для y_train применяется one-hot encoding и первоначальному прогнозу приcваиваются значения 0 для каждого класса;
2) прогнозы преобразуются в вероятности с помощью softmax-функции;
3) рассчитываются остатки модели на основе антиградиента функции потерь и вероятностей (а также веса в случае LogitBoost);
4) регрессионное дерево обучается на X_train и остатках (а в случае LogitBoost ещё присваиваются веса), далее делается прогноз на X_train;
5) для каждого листа в дереве рассчитываются коэффициенты $\gamma$ на основе остатков, взятых по позициям наблюдений, попавших в определённый в листовой узел;
6) полученные прогнозы для каждого класса и сумма коэффициентов $\gamma$ добавляются к первоначальным;
7) шаги 2-6 повторяются для каждого дерева в каждом классе;
8) после обучения всех моделей создаётся первоначальный прогноз из шага 1;
9) далее делаются прогнозы для X_test на обученных деревьях по каждому классу и добавляются к первоначальным;
10) классы с максимальной суммой и будут конечным прогнозом.

Формулы для расчётов

Функция потерь:

$L(\{y_k, F_k(x)\}_{1}^{K}) = -\sum\limits_{k=1}^{K} y_k \ log \ p_k(x)$

Вероятность каждого класса:

$p_k(x) = softmax(F_k(x)) = \frac{e^{F_k(x)}}{\sum\limits_{l=1}^{K} e^{F_l(x)}}$

Остатки:

$r_{ik} = -\left[\frac{\partial L(\{y_{il}, F_l(x_i)\}_{l=1}^{K})}{\partial F_k(x_i)}\right]_ {\{F_l(x) = F_{l,m-1}(x)\}_{1}^{K}} = y_{ik} - p_{k,m-1}(x_i)$

Коэффициент $\gamma$ :

$\gamma_{jkm} = \frac{K-1}{K} \frac{\sum_{x_i \in R_{jkm}} r_{ik}} {\sum_{x_i \in R_{jkm}} |r_{ik}| (1 - |r_{ik}|)}$

Веса для K-class LogitBoost:

Остатки для K-class LogitBoost:

$r_{ik} = \frac{K-1}{K} \frac{y_{ik} - p_k(x_i)}{w_k(x_i)}$

Импорт необходимых библиотек

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import load_diabetes
from sklearn.preprocessing import LabelEncoder
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, mean_absolute_percentage_error
from sklearn.tree import DecisionTreeRegressor
from sklearn.ensemble import GradientBoostingClassifier, GradientBoostingRegressor
from sklearn.ensemble import HistGradientBoostingClassifier, HistGradientBoostingRegressor
from mlxtend.plotting import plot_decision_regions

Реализация на Python с нуля

class GBMClassifier:
    def __init__(self, logitboost=False, learning_rate=0.1, n_estimators=100,
                 max_depth=3, random_state=0):
        self.logitboost = logitboost
        self.learning_rate = learning_rate
        self.n_estimators = n_estimators
        self.max_depth = max_depth
        self.random_state = random_state

    def _softmax(self, predictions):
        exp = np.exp(predictions)

        return exp / np.sum(exp, axis=1, keepdims=True)

    def _compute_gammas(self, residuals, leaf_indexes, eps=1e-4):
        gammas = []

        for j in np.unique(leaf_indexes):
            x_i = np.where(leaf_indexes == j)
            numerator = np.sum(residuals[x_i])
            norm_residuals_xi = np.linalg.norm(residuals[x_i]) + eps
            denominator = np.sum(norm_residuals_xi * (1 - norm_residuals_xi))
            gamma = (self.K - 1) / self.K * numerator / denominator
            gammas.append(gamma)

        return gammas

    def fit(self, X, y):
        self.K = len(np.unique(y))
        self.trees = {k: [] for k in range(self.K)}
        one_hot_y = pd.get_dummies(y).to_numpy()   # one-hot encoding
        predictions = np.zeros(one_hot_y.shape)

        for _ in range(self.n_estimators):
            probabilities = self._softmax(predictions)

            for k in range(self.K):
                if self.logitboost:   # based on K-class LogitBoost
                    numerator = (one_hot_y.T[k] - probabilities.T[k])
                    denominator = probabilities.T[k] * (1 - probabilities.T[k])
                    residuals = (self.K - 1) / self.K * numerator / denominator
                    weights = denominator
                else:
                    residuals = one_hot_y.T[k] - probabilities.T[k]
                    weights = None

                tree = DecisionTreeRegressor(criterion='friedman_mse', max_depth=self.max_depth,
                                             random_state=self.random_state)
                tree.fit(X, residuals, sample_weight=weights)
                self.trees[k].append(tree)

                leaf_indexes = tree.apply(X)
                gammas = [] if self.logitboost else self._compute_gammas(residuals, leaf_indexes)
                predictions.T[k] += self.learning_rate * tree.predict(X) + np.sum(gammas)

    def predict(self, samples):
        predictions = np.zeros((len(samples), self.K))

        for i in range(self.n_estimators):
            for k in range(self.K):
                predictions.T[k] += self.learning_rate * self.trees[k][i].predict(samples)

        return np.argmax(predictions, axis=1)

class GBMRegressor:
    def __init__(self, learning_rate=0.1, n_estimators=100, max_depth=3, random_state=0):
        self.learning_rate = learning_rate
        self.n_estimators = n_estimators
        self.max_depth = max_depth
        self.random_state = random_state
        self.trees = []

    def fit(self, X, y):
        self.initial_leaf = y.mean()
        predictions = np.zeros(len(y)) + self.initial_leaf

        for _ in range(self.n_estimators):
            residuals = y - predictions
            tree = DecisionTreeRegressor(criterion='friedman_mse', max_depth=self.max_depth,
                                         random_state=self.random_state)
            tree.fit(X, residuals)
            predictions += self.learning_rate * tree.predict(X)
            self.trees.append(tree)

    def predict(self, samples):
        predictions = np.zeros(len(samples)) + self.initial_leaf

        for i in range(self.n_estimators):
            predictions += self.learning_rate * self.trees[i].predict(samples)

        return predictions

Код для отрисовки решающих границ

def decision_boundary_plot(X, y, X_train, y_train, clf, feature_indexes, title=None):
    feature1_name, feature2_name = X.columns[feature_indexes]
    X_feature_columns = X.values[:, feature_indexes]
    X_train_feature_columns = X_train.values[:, feature_indexes]
    clf.fit(X_train_feature_columns, y_train.values)

    plot_decision_regions(X=X_feature_columns, y=y.values, clf=clf)
    plt.xlabel(feature1_name)
    plt.ylabel(feature2_name)
    plt.title(title)

Загрузка датасетов

Для обучения моделей будет использован Glass Classification датасет, где необходимо верно определить тип стекла по его признакам. В случае регрессии используется Diabetes датасет из scikit-learn.

Данные ниже будут использоваться в примерах для всех модификаций градиентного бустинга.

df_path = "/content/drive/MyDrive/glass.csv"
glass_df = pd.read_csv(df_path)
X1, y1 = glass_df.iloc[:, :-1], glass_df.iloc[:, -1]
y1 = pd.Series(LabelEncoder().fit_transform(y1))
X1_train, X1_test, y1_train, y1_test = train_test_split(X1, y1, random_state=0)
print(glass_df)


          RI     Na    Mg    Al     Si     K    Ca    Ba   Fe  Type
0    1.52101  13.64  4.49  1.10  71.78  0.06  8.75  0.00  0.0     1
1    1.51761  13.89  3.60  1.36  72.73  0.48  7.83  0.00  0.0     1
2    1.51618  13.53  3.55  1.54  72.99  0.39  7.78  0.00  0.0     1
3    1.51766  13.21  3.69  1.29  72.61  0.57  8.22  0.00  0.0     1
4    1.51742  13.27  3.62  1.24  73.08  0.55  8.07  0.00  0.0     1
..       ...    ...   ...   ...    ...   ...   ...   ...  ...   ...
209  1.51623  14.14  0.00  2.88  72.61  0.08  9.18  1.06  0.0     7
210  1.51685  14.92  0.00  1.99  73.06  0.00  8.40  1.59  0.0     7
211  1.52065  14.36  0.00  2.02  73.42  0.00  8.44  1.64  0.0     7
212  1.51651  14.38  0.00  1.94  73.61  0.00  8.48  1.57  0.0     7
213  1.51711  14.23  0.00  2.08  73.36  0.00  8.62  1.67  0.0     7

[214 rows x 10 columns]

X2, y2 = load_diabetes(return_X_y=True, as_frame=True)
X2_train, X2_test, y2_train, y2_test = train_test_split(X2, y2, random_state=0)
print(X2, y2, sep='\n')


          age       sex       bmi        bp        s1        s2        s3  \
0    0.038076  0.050680  0.061696  0.021872 -0.044223 -0.034821 -0.043401   
1   -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163  0.074412   
2    0.085299  0.050680  0.044451 -0.005670 -0.045599 -0.034194 -0.032356   
3   -0.089063 -0.044642 -0.011595 -0.036656  0.012191  0.024991 -0.036038   
4    0.005383 -0.044642 -0.036385  0.021872  0.003935  0.015596  0.008142   
..        ...       ...       ...       ...       ...       ...       ...   
437  0.041708  0.050680  0.019662  0.059744 -0.005697 -0.002566 -0.028674   
438 -0.005515  0.050680 -0.015906 -0.067642  0.049341  0.079165 -0.028674   
439  0.041708  0.050680 -0.015906  0.017293 -0.037344 -0.013840 -0.024993   
440 -0.045472 -0.044642  0.039062  0.001215  0.016318  0.015283 -0.028674   
441 -0.045472 -0.044642 -0.073030 -0.081413  0.083740  0.027809  0.173816   

           s4        s5        s6  
0   -0.002592  0.019907 -0.017646  
1   -0.039493 -0.068332 -0.092204  
2   -0.002592  0.002861 -0.025930  
3    0.034309  0.022688 -0.009362  
4   -0.002592 -0.031988 -0.046641  
..        ...       ...       ...  
437 -0.002592  0.031193  0.007207  
438  0.034309 -0.018114  0.044485  
439 -0.011080 -0.046883  0.015491  
440  0.026560  0.044529 -0.025930  
441 -0.039493 -0.004222  0.003064  

[442 rows x 10 columns]
0      151.0
1       75.0
2      141.0
3      206.0
4      135.0
       ...  
437    178.0
438    104.0
439    132.0
440    220.0
441     57.0
Name: target, Length: 442, dtype: float64

Обучение моделей и оценка полученных результатов

В случае классификации ручная реализация немного отличается в плане точности от scikit-learn — это связано с тем, что в последней применяется более усложнённый подход для прогнозирования и расчёта остатков, но суть остаётся прежней, и в большинстве случаев работает примерно также как и ручная реализация, особенно в сравнении с LogitBoost модификацией.

В случае регрессии, ошибка в ручной реализации даже немного ниже, чем в scikit-learn — различия незначительны.

Также стоит отметить, что в scikit-learn есть особая версия градиентного бустинга — HistGradientBoosting на основе LightGBM, предназначенная для работы с большими наборами данных, которая отрабатывает гораздо быстрее и чаще лучше, чем классический градиентный бустинг.

Полученные результаты приведены ниже.

GBMClassifier

gbc = GBMClassifier(random_state=0)
gbc.fit(X1_train, y1_train)
gbc_pred_res = gbc.predict(X1_test)
gbc_accuracy = accuracy_score(gbc_pred_res, y1_test)
print(f'gbc accuracy: {gbc_accuracy}')
print(gbc_pred_res)


gbc accuracy: 0.6111111111111112
[5 0 1 4 1 1 0 1 1 1 1 0 1 1 1 5 0 1 1 1 5 0 5 5 1 0 5 0 1 0 0 4 1 0 0 0 0
 0 0 5 1 4 1 0 0 1 0 1 0 1 0 3 5 0]

GBMClassifier с концепцией LogitBoost

logit_bc = GBMClassifier(logitboost=True, random_state=0)
logit_bc.fit(X1_train, y1_train)
logit_bc_pred_res = logit_bc.predict(X1_test)
logit_bc_accuracy = accuracy_score(logit_bc_pred_res, y1_test)
print(f'logit_gbc accuracy: {logit_bc_accuracy}')
print(logit_bc_pred_res)


logit_gbc accuracy: 0.6666666666666666
[5 0 1 4 1 1 0 1 1 1 1 0 0 1 1 5 2 1 1 0 3 0 5 1 2 0 5 0 0 1 0 0 1 0 0 0 0
 2 0 5 1 4 1 0 1 1 0 1 0 1 0 1 5 0]

GradientBoostingClassifier (scikit-learn)

sk_gbc = GradientBoostingClassifier(random_state=0)
sk_gbc.fit(X1_train, y1_train)
sk_gbc_pred_res = sk_gbc.predict(X1_test)
sk_gbc_accuracy = accuracy_score(sk_gbc_pred_res, y1_test)
print(f'sk_gbc accuracy: {sk_gbc_accuracy}')
print(sk_gbc_pred_res)

feature_indexes = [1, 3]
title1 = 'GradientBoostingClassifier surface'
decision_boundary_plot(X1, y1, X1_train, y1_train, sk_gbc, feature_indexes, title1)


sk_gbc accuracy: 0.6666666666666666
[5 0 1 4 1 1 0 1 1 1 1 0 1 1 1 5 2 1 2 0 1 0 5 5 0 0 5 0 0 1 0 0 1 0 1 0 0
 0 0 5 1 1 1 0 1 1 0 1 0 1 0 1 5 0]

HistGradientBoostingClassifier (scikit-learn)

sk_hist_gbc = HistGradientBoostingClassifier(random_state=0)
sk_hist_gbc.fit(X1_train, y1_train)
sk_hist_gbc_pred_res = sk_hist_gbc.predict(X1_test)
sk_hist_gbc_accuracy = accuracy_score(sk_hist_gbc_pred_res, y1_test)
print(f'sk_hist_gbc accuracy: {sk_hist_gbc_accuracy}')
print(sk_hist_gbc_pred_res)

feature_indexes = [1, 3]
title2 = 'HistGradientBoostingClassifier surface'
decision_boundary_plot(X1, y1, X1_train, y1_train, sk_hist_gbc, feature_indexes, title2)


sk_hist_gbc accuracy: 0.7407407407407407
[5 0 1 4 1 1 0 1 1 1 0 1 0 1 1 5 2 1 0 2 3 0 5 5 0 0 5 0 1 1 0 0 1 0 0 0 0
 2 0 5 1 4 1 0 0 1 0 1 0 1 0 1 5 0]

GBMRegressor

gbr = GBMRegressor(random_state=0)
gbr.fit(X2_train, y2_train)
gbr_pred_res = gbr.predict(X2_test)
mape = mean_absolute_percentage_error(gbr_pred_res, y2_test)
print(f'gbr mape: {mape}')
print(gbr_pred_res)


gbr mape: 0.3422881238725283
[255.26058697 236.87383554 189.22369747 111.4291292  195.31958776
 249.2293251   97.46956406 205.91110801 133.47952304 240.88679883
 187.19018483 171.09963906 132.63933991  86.28964353 286.56077589
 105.78347251 161.94686043  72.58069452 105.92470096 236.52718059
 178.31146418 127.93036968 164.16563703 147.68681371 229.72747212
 194.16656023 142.44300193  68.79177464 237.21638657 163.36730299
 228.0338107   85.82843049 122.42781509 153.99332065 133.44848601
 159.00754731 151.98981608 147.1238119   88.56372077 200.84785209
 111.32129613 157.60108633 137.94395538 173.39402287 176.29284757
  62.85019316 109.646804   124.14982054  83.45697583 266.40618239
 141.2307366   42.05033124 163.57898214 149.92213387 230.37326368
 226.98842404 176.95426024 128.73302071  94.7641018  180.13853236
 242.31821245 147.52903035 130.45931832  97.32617479 246.70709949
 155.26338705  88.36785447 243.39330218 215.93042351  57.89243255
  87.76236479 138.21222825 101.23449416 140.80521012 128.63575744
 180.15062966 126.14000544 220.28212417 272.05642136 203.4384734
 135.96206295 180.87259854  55.62066017 241.84218009 137.19320157
  85.57441147 154.16763601 198.15465153 107.34659467 158.72672412
 102.17554103 114.4602227   70.44016611 165.66282053 108.02991765
  87.88855231 218.47152891 250.1208086  131.93276827 164.8880371
 174.16393905 119.21512394 150.9405975   93.44225978 234.7444088
 139.46581273 248.28728947 276.8291188  121.36081625  77.12248695
 252.1021757 ]

GradientBoostingRegressor (scikit-learn)

sk_gbr = GradientBoostingRegressor(random_state=0)
sk_gbr.fit(X2_train, y2_train)
sk_gbr_pred_res = sk_gbr.predict(X2_test)
sk_mape = mean_absolute_percentage_error(sk_gbr_pred_res, y2_test)
print(f'sk_gbr mape: {sk_mape}')
print(sk_gbr_pred_res)


sk_gbr mape: 0.34315075601365186
[255.26058697 236.87383554 189.22369747 111.4291292  195.31958776
 249.2293251   97.46956406 205.91110801 133.47952304 240.88679883
 187.19018483 171.09963906 132.63933991  86.28964353 286.56077589
 105.78347251 161.94686043  72.58069452 105.92470096 236.52718059
 182.08417504 127.93036968 164.16563703 147.68681371 229.72747212
 194.16656023 142.44300193  68.79177464 237.21638657 163.36730299
 223.14955275  85.82843049 122.42781509 153.99332065 133.44848601
 159.00754731 151.98981608 147.1238119   88.56372077 200.84785209
 117.71059889 157.60108633 137.94395538 173.39402287 176.29284757
  62.85019316 109.646804   124.14982054  83.45697583 266.40618239
 141.2307366   42.05033124 163.57898214 149.92213387 230.37326368
 226.98842404 176.95426024 128.73302071  94.7641018  180.13853236
 242.31821245 147.52903035 131.71442058  97.32617479 246.70709949
 155.26338705  88.36785447 243.39330218 215.93042351  54.04270734
  87.76236479 138.21222825 101.23449416 140.80521012 128.63575744
 180.15062966 126.14000544 220.28212417 272.05642136 203.4384734
 135.96206295 180.87259854  55.62066017 241.84218009 137.19320157
  85.57441147 154.16763601 198.15465153 107.34659467 158.72672412
 102.17554103 114.4602227   70.44016611 165.66282053 108.02991765
  87.88855231 218.47152891 247.93843617 131.93276827 164.8880371
 174.16393905 119.21512394 150.9405975   93.44225978 234.7444088
 139.46581273 248.28728947 286.90898175 121.36081625  77.12248695
 252.1021757 ]

HistGradientBoostingRegressor (scikit-learn)

sk_hist_gbr = HistGradientBoostingRegressor(random_state=0)
sk_hist_gbr.fit(X2_train, y2_train)
sk_hist_gbr_pred_res = sk_hist_gbr.predict(X2_test)
sk_hist_mape = mean_absolute_percentage_error(sk_hist_gbr_pred_res, y2_test)
print(f'sk_hist_gbr mape: {sk_hist_mape}')
print(sk_hist_gbr_pred_res)


sk_hist_gbr mape: 0.3625770694795175
[264.59007545 243.59190524 180.62442773 108.53165744 195.17695513
 258.1710931  112.67894454 239.18006052 144.50027011 244.02461776
 180.19087697 171.2628973  142.6966707   94.26236013 301.44493762
  90.25622203 154.82566511  75.43291346  96.36987316 230.14565012
 196.50928346 134.41863815 167.28719774 118.51218378 209.75431111
 176.46248808 113.40188129  68.47515467 248.57638999 116.15751993
 195.54397416  59.94733366 153.03012884 165.84819847 135.95402508
 133.54279177 190.26058998 153.08963938  86.65214731 185.07312005
 110.00197459 142.99434304 111.32566034 205.63519803 163.76035901
  68.26003406 118.15074567 101.01137587  57.54356002 247.29839792
 140.32714196  41.87878548 149.89720974 189.08931404 251.48016218
 175.76119949 160.38118455 110.76716142 107.00114228 154.75409577
 256.3194536  148.8935956  119.32752592  78.65118163 252.18315433
 122.833807    92.10033912 219.56310647 199.35553751  87.27114699
  78.83529151 114.14943246  86.07433503 110.44443265 126.1152782
 193.58960355 125.06171193 207.62012728 297.41734601 206.57210109
 121.92170504 194.37322797  69.66978916 260.97214455  99.77944002
 104.34927662 131.51094535 200.0857846  114.70076625 144.92225838
 107.08233694  84.70304021  65.20782844 156.77203859  93.87016441
 117.10361355 213.79169982 258.68468943 129.45477593 140.06443861
 176.72311312 107.95798342 172.45179867 115.75603211 240.83612061
 102.2339954  249.6969811  293.80624063 110.47825419  73.86099524
 238.42985813]

Преимущества и недостатки градиентного бустинга (GBM)

Преимущества:

высокая точность;
хорошо работает с неоднородными данными;
лежит в основе других модификаций градиентного бустинга.

Недостатки:

низкая скорость обучения при работе с большими датасетами;
отсутствие возможности работы с категориальными признаками;
возможность переобучения из-за плохой предобработки данных.

Стоит отметить, что вышеперечисленные недостатки были устранены частично либо полностью в модификациях градиентного бустинга, про которые сейчас и пойдёт речь.

Дополнительные источники

Статья «Greedy Function Approximation: A Gradient Boosting Machine», Jerome H. Friedman.

Документация:

Лекции:

Пошаговое построение Gradient Boosting:

Особенности XGBoost

XGBoost (Extreme Gradient Boosting) является, пожалуй, самой популярной модификацией градиентного бустинга на сегодняшний день, с помощью которой было выиграно множество соревнований на Kaggle. Рассмотрим причины по которым так произошло.

В отличие от GBM в XGboost изначальный прогноз регрессионного дерева устанавливается f_0 (x) = 0.5 и вместо пней с глубиной 3 берутся более глубокие деревья с листьями в диапазоне от 8 до 32 как в случае регрессии, так и классификации, а к функции потерь добавляется регуляризация (L1 или L2 на выбор), которая штрафует дерево с высокой суммой нормы значений в листьях. Данная сумма представлена в виде целевой функции, расчёт значений которой аппроксимируется разложением в ряд Тейлора 2-го порядка.

Формулы для расчётов

Целевая функция:

$Obj^{\ t} = \sum\limits_{i=1}^{N} L(y_i, \hat{y_i}^{(t-1)} + f_t(x_i)) + \Omega(f_t)$

L2-регуляризация:

$\Omega(f_t) = \gamma \ T + \frac{1}{2} \lambda||w||^2$

Аппроксимация целевой функции разложением в ряд Тейлора 2-го порядка:

$Obj^{\ t} \approx \sum\limits_{i=1}^{N} [L(y_i, \hat{y_i}^{(t-1)}) + g_i f_t(x_i) + \frac{1}{2} h_i f_t^2(x_i) ] + \gamma \ T + \frac{1}{2} \lambda \sum\limits_{j=1}^{T} w_j^2 = \\ = \sum\limits_{j=1}^{T} [(\sum\limits_{i \in I_j}g_i) w_j + \frac{1}{2} (\sum\limits_{i \in I_j}h_i + \lambda) w_j^2 ] + \gamma \ T$

Где:

градиент первого порядка: ;
градиент второго порядка (гессиан): ;
параметры регуляризации: $\gamma, \lambda$ .

Приближение второго порядка удобно с вычислительной точки зрения, поскольку большинство членов одинаковы на каждой отдельной итерации и большая часть выражения может быть вычислена один раз и повторно использована как константа для всех остальных разбиений, и в таком случае единственное, что остаётся вычислить — это f_t(x_i) и $\Omega(f_t)$ .

Оптимальное значение веса j-го листового узла в дереве рассчитывается следующим образом:

$w^*_j = -\frac{\sum_{i \in I_j} g_i}{\sum_{i \in I_j} h_i + \lambda}$

Мера загрязнённости представляет из себя качество структуры дерева q и рассчитывается следующим образом:

$Obj^{\ t} = -\frac{1}{2} \sum\limits_{j=1}^{T} \frac{(\sum_{i \in I_j} g_i)^2}{\sum_{i \in I_j} h_i + \lambda} + \gamma \ T$

Чем меньше это значение, тем лучше структура дерева.

Поскольку перечисление всевозможных древовидных структур и выбор наилучшей весьма осложнён, мы можем оптимизировать данную задачу, добавляя по одному разбиению узла дерева за раз. В частности, мы итеративно добавляем ветви к дереву, используя жадный алгоритм, а информационный прирост будет выглядеть следующим образом:

$gain = \frac{1}{2} \left[\frac{(\sum_{i \in I_L} g_i)^2}{\sum_{i \in I_L} h_i + \lambda} + \frac{(\sum_{i \in I_R} g_i)^2}{\sum_{i \in I_R} h_i + \lambda} - \frac{(\sum_{i \in I} g_i)^2}{\sum_{i \in I} h_i + \lambda} \right] - \gamma$

Информационный прирост будет показывать изменение чистоты узла после его разбиения. Его максимальное значение будет соответствовать наилучшему пороговому значению (критерию разбиения) узла в дереве.

Стоит также упомянуть, что в XGBoost поддерживается выбор линейных моделей в качестве базовых, но, в целом, они работают хуже деревьев.

Дополнительные оптимизации в XGBoost

Weighted quantile sketch

В случае работы с большими наборами данных в XGBoost используется приближённый жадный алгоритм. Это означает, что вместо тестирования всех возможных пороговых значений мы тестируем только квантили. Используя распараллеливание для разделения набора данных и создания ветвей в каждом дереве независимо друг от друга чтобы несколько ядер могли работать с ними одновременно, алгоритм взвешенных квантилей (weighted quantile sketch) объединяет данные в приближённую гистограмму, разделённую на взвешенные квантили, которые помещают наблюдения с прогнозами низкой достоверности в квантили с меньшим количеством наблюдений.

Cache-aware access & out-of-core computing

Для более быстрого вычисления прогнозов градиенты и гессианы хранятся в кэш-памяти (cache-aware access), а в случае с датасетами большого размера, когда недостаточно кэш и оперативной памяти, задействуется память из жёсткого диска. Учитывая, что чтение данных на жёстком диске выполняется гораздо медленнее чем в кэш-памяти, для ускоренной обработки производится их компрессия. Данные хранятся в единицах памяти, называемых блоками, информация в которых хранится в формате сжатых столбцов, отсортированных по соответствующим значениям параллельно с использованием всех доступных ядер ЦП, а распаковка каждого блока осуществляется в независимом потоке при загрузке в память. Данная техника называется "вычисление вне ядра" (out-of-core computing). При наличии нескольких жёстких дисков, применяется параллельное сегментирование блоков для каждого жёсткого диска (sharding).

При использовании сжатых данных необходимо учитывать, что процесс сжатия и распаковки занимает дополнительное время, поэтому выбор алгоритма сжатия (с потерями и без) и его параметров может повлиять на производительность в целом, однако это всё равно значительно быстрее чтения без сжатия.

Sparsity-aware split finding

В XGboost также поддерживается работа с пропусками. Суть заключается в следующем: из исходного датасета убираются наблюдения с пропусками и представляются как отдельный датасет. После построения дерева для наблюдений без пропусков рассчитываются их остатки, далее — остатки для наблюдений с пропусками, которые присоединяются к остаткам дерева как для левого, так и для правого узла. В конце рассчитывается информационный прирост (gain) для каждого узла в дереве: выбирается порог для разбиения с максимальным приростом. Данная техника называется "поиск разбиения с учётом разряженности" (sparsity-aware split finding).

Обучение на GPU

Для ускорения процесса обучения в XGBoost реализована поддержка GPU с помощью параметров device="cuda" и tree_method="gpu_hist". Также стоит отметить, что в данном алгоритме поддерживается полностью распределённое обучение на GPU с использованием Dask, Spark и PySpark.

Пакетная реализация XGBoost и оценка полученных результатов

Благодаря вышеуказанным оптимизациям и особенностям XGBoost работает лучше классической реализации, что видно на примере классификации, однако на примере регрессии в данном случае результат оказался хуже. Если хорошо подготовить данные и поэкспериментировать с настройкой гиперпараметров, XGBoost будет работать гораздо лучше как в случае регрессии, так и классификации.

XGBClassifier

from xgboost import XGBClassifier, XGBRegressor

xgbc = XGBClassifier(seed=0)
xgbc.fit(X1_train, y1_train)
xgbc_pred_res = xgbc.predict(X1_test)
xgbc_accuracy = accuracy_score(xgbc_pred_res, y1_test)
print(f'xgbc accuracy: {xgbc_accuracy}')
print(xgbc_pred_res)

feature_indexes = [1, 3]
title2 = 'XGBClassifier surface'
decision_boundary_plot(X1, y1, X1_train, y1_train, xgbc, feature_indexes, title2)


xgbc accuracy: 0.6851851851851852
[5 0 1 4 1 1 0 1 1 1 3 0 1 1 1 5 2 1 1 2 3 0 5 5 0 0 5 0 0 1 0 0 1 0 0 0 0
 0 0 5 1 4 1 0 1 1 0 1 0 1 0 1 5 0]

XGBRegressor

xgbr = XGBRegressor(seed=0)
xgbr.fit(X2_train, y2_train)
xgbr_pred_res = xgbr.predict(X2_test)
xgbr_mape = mean_absolute_percentage_error(xgbr_pred_res, y2_test)
print(f'xgbr mape: {xgbr_mape}')
print(xgbr_pred_res)


xgbr mape: 0.3781388070785457
[281.3304   241.21165  212.13124  136.89372  144.54208  261.7871
 125.257454 236.16089  199.79964  250.18103  188.50882  126.724464
 161.2112    73.98386  302.50272   97.35103  160.85774   67.10394
  96.0406   284.72873  181.48717  117.764626 182.91393  127.76686
 229.30229  173.58592  170.03932   76.73085  240.7698   117.70699
 224.36049   63.628925 124.27327  142.07358  173.09418  139.11557
 163.61208   92.8561    95.91142  217.65016  112.03522  122.800545
 110.06953  181.34201  159.39062   61.97588  114.534805 145.20259
  84.905815 284.77567  195.29976   45.550606  92.54941  180.4689
 279.12097  241.1343   177.77785  130.43887  159.53189  158.2313
 253.25339  181.86093  120.71679   90.604706 274.5059   140.21674
  92.80314  211.71936  233.20622  110.791824  67.89235  133.62137
 123.05923  102.70884  167.2115   159.32262  131.7305   243.41493
 254.97531  210.0554   130.00981  222.21094   52.864147 251.23187
 118.602684  87.89112  121.147095 218.15724   90.9274    91.69777
 101.95428   85.79966   79.59963  155.879    118.25745   99.5975
 231.70824  189.6652   121.97507  147.51166  152.10051  102.239395
 177.74615  107.55845  271.80927  121.41044  232.97308  292.89096
 129.39447   60.501278 259.46295 ]

Преимущества и недостатки XGBoost

Преимущества:

относительно высокая скорость обучения и точность прогнозов;
возможность работы с пропусками;
гибкость в конфигурации из-за большого количества гиперпараметров.

Недостатки:

сложность в конфигурации из-за большого количества гиперпараметров;
на данный момент отсутствует полноценная (присутствует экспериментальная) возможность работы с категориальными признаками, что может сильно снизить производительность при кодировании больших объёмов данных.

Дополнительные источники

Статья «XGBoost: A Scalable Tree Boosting System», Tianqi Chen, Carlos Guestrin.

Документация.

Лекции:

один;
два.

Пошаговое построение XGBoost:

Особенности CatBoost

CatBoost (Categorical Boosting) — более эффективная реализация градиентного бустинга от компании Яндекс, особенностью которой является возможность работы с категориальными признаками без их предварительной обработки. Разберёмся подробнее как это происходит.

Ordered target (CatBoost) encoding

При кодировании категориальных признаков к бустингам применяется один из нескольких классических подходов:

target encoding;
one-hot encoding (хорошо работает лишь в том случае, когда в признаках содержится небольшое количество значений);
feature hashing в несколько корзин (исходные данные преобразуются в уникальную последовательность символов (хэш-значения), которые разбиваются на группы (корзины) и обрабатываются параллельно с последующим применением target или one-hot encoding);
mean target encoding (рассчитывается новое значение для текущего категориального признака как среднее значение целевой переменной по датасету);
leave-one-out (рассчитывается среднее значение целевой переменной по всем объектам кроме текущего);
leave-bucket-out (рассчитывается среднее значение целевой переменной на одной части данных и применяется для оставшихся других);

Однако все вышеперечисленные способы так или иначе приводят к утечке данных и переобучению, и данную проблему можно частично решить с применением mean target encoding на отложенной выборке, что работает заметно лучше, но такой способ не идеален так как остаётся меньше данных для обучения и вычисления статистик по категориальным признакам.

В CatBoost применяется модифицированный подход к mean target encoding, называемый Ordered target (CatBoost) encoding, который состоит из 3-х нижеперечисленных этапов.

Случайная перестановка

Образцы в наборе данных перемешиваются случайным образом, что позволяет создать более сбалансированный набор данных и снизить переобучение.

Статистики «по прошлому»

После случайной перестановки рассчитывается новое значение для текущего категориального признака следующим образом:

$CTR = \frac{TargetSum + Prior}{TotalCount + 1}$

Prior — константа, определяемая как среднее арифметическое целевых значений.

TargetSum — сумма целевых значений для конкретного категориального признака до текущего момента.

TotalCount — количество всех наблюдений для конкретного категориального признака до текущего момента.

Данная формула может быть применима как для регрессии, так и для мультиклассификации.

Пошаговый пример с нуля для мультиклассификации

!pip install category_encoders

from category_encoders.cat_boost import CatBoostEncoder

train = pd.DataFrame({"color": ["red", "blue", "black", "black", "blue", "blue", "red", "blue"]})
target = pd.Series([2, 1, 2, 1, 0, 3, 0, 1])

cbe_encoder = CatBoostEncoder()
train_cbe = cbe_encoder.fit_transform(train, target)
prior = target.mean()

print(f'prior: {prior}', '', sep='\n')
print(train_cbe)


prior: 1.25

    color
0  1.2500
1  1.2500
2  1.2500
3  1.6250
4  1.1250
5  0.7500
6  1.6250
7  1.3125

В случае c числовыми признаками создаётся набор меток с помощью квантования и производится их бинаризация на k классов: все значения до границы (метки) относятся к классу 0, а после к классу 1. Далее процедура схожа со случаем выше.

В CatBoost поддерживаются следующие виды квантования:

мода;
медианная сетка;
равномерная сетка + квантили (размер квантования уменьшается вдвое и разбиения (пороговые значения) объединяются по одному из двух способов: медиана или равномерная сетка);
MaxLogSum — максимизируется значение следующего выражения внутри каждого сегмента:

$\sum\limits_{i=1}^{n} log \ w_i$

MinEntropy — минимизируется значение следующего выражения внутри каждого сегмента:

$\sum\limits_{i=1}^{n} w_i \ log \ w_i$

GreedyLogSum — максимизируется аппроксимация жадным способом следующего выражения внутри каждого сегмента:

$\sum\limits_{i=1}^{n} log \ w_i$

где n — число различных объектов в сегменте, w (weight) — число повторений объекта в сегменте.

Комбинация категориальных признаков

В CatBoost используется комбинация категориальных признаков (например, красный диван, синий диван, синий стул и так далее), что позволяет модели учитывать неочевидные взаимосвязи между ними и улучшить качество итоговых прогнозов в целом. Для избегания экспоненциального роста комбинаций категориальных признаков, их создание происходит не перед началом обучения, а в момент построения каждого дерева жадным алгоритмом отдельно.

Структура решающих деревьев и упорядоченный бустинг

В качестве базовых моделей в CatBoost используются симметричные односторонние деревья, имеющие одинаковую глубину и ширину. Создатели алгоритма считают, что такой подход позволяет ускорить обучение и создавать деревья, которые менее подвержены переобучению.

Для нахождения наилучшего критерия разбиения в узле используется косинусное сходство — его максимальное значение будет соответствовать лучшему критерию:

$Cosine \ Similarity = \frac{ \sum\limits_{i=1}^{n} A_i B_i}{\sqrt{\sum\limits_{i=1}^{n} A_i^2} \sqrt{\sum\limits_{i=1}^{n} B_i^2}}$

где A — вектор с остаточными ошибками, B — вектор с прогнозами в листовых узлах.

Проблема классического бустинга заключается в том, что прогнозы базовых моделей могут иметь высокое смещение, что в конечном счёте приводит к переобучению модели в целом — это обусловлено тем, что обучение и оценка деревьев производится на одинаковом наборе данных (X_train). Данная проблема решается с помощью метода линейной аппроксимации упорядоченного бустинга (Ordered Boosting), суть которого заключается в следующем: данные перемешиваются случайным образом и после чего текущее дерево обучается на m-1 образцах с учётом остатков предыдущего, что очень похоже на принцип в ordered target encoding, то есть изначально берётся один образец из набора данных и модель учится на всех образцах до него, то есть на нулях, далее берётся два образца и модель учится на одном, после чего рассчитываются остатки, которые будут использованы для следующей модели и так далее. Такой подход позволяет произвести обучение дерева со сложностью O(log(m)) вместо O(m^2) .

Структура симметричного одностороннего дерева

Дополнительные возможности CatBoost

Работа с пропусками

Поддерживаются следующие режимы обработки пропусков:

"Forbidden" — пропуски интерпретируются как ошибки.
"Min" — пропуски обрабатываются как минимальное значение (меньшее, чем все остальные значения) для объекта.
"Max" — пропуски обрабатываются как максимальное значение (превышающее все остальные значения) для объекта.

Режим обработки по умолчанию — Min. Также при выборе деревьев учитывается разбиение, отделяющее пропущенные значения от всех остальных.

Snapshots

Данный параметр (save_snapshot=True) позволяет создавать резервные копии промежуточных результатов. Если происходит неожиданное прерывание обучения (например, случайное выключение компьютера), то оно может быть продолжено из сохранённого состояния и в таком случае не нужно повторять завершённые итерации построения деревьев.

Обучение на GPU

В CatBoost возможно обучение не только на нескольких GPU, но и сразу на нескольких серверах с GPU, что фактически позволяет запустить распределённое обучение и использовать датасеты любого размера. Данная процедура позволяет значительно ускорить работу алгоритма: чем больше датасет, тем больше будет прирост в производительности в сравнении с обучением на CPU. Для того чтобы этим воспользоваться достаточно указать task_type="GPU".

Пакетная реализация CatBoost и оценка полученных результатов

Как можно заметить из примера классификации, не смотря на большое количество улучшений, CatBoost далеко не всегда показывает высокие результаты в сравнении с другими реализациями градиентного бустинга, как это заявляют его разработчики, особенно заметна разница в случае с несбалансированными наборами данных. Однако, стоит отметить, что в случае хорошей подготовки данных, при прочих равных, в ряде случаев CatBoost будет отличаться от других модификаций немного более высокой точностью.

В случае регрессии, когда нет явно выраженной проблемы как в случае выше, CatBoost справляется довольно хорошо.

Полученные результаты приведены ниже.

!pip install catboost

CatBoostClassifier

from catboost import CatBoostClassifier, CatBoostRegressor

cb_clf = CatBoostClassifier(random_seed=0, logging_level='Silent')
cb_clf.fit(X1_train, y1_train)
cb_clf_pred_res = cb_clf.predict(X1_test).squeeze()   # remove all single-dimensional entries
cb_clf_accuracy = accuracy_score(cb_clf_pred_res, y1_test)
print(f'cb_clf accuracy: {cb_clf_accuracy}')
print(cb_clf_pred_res)

feature_indexes = [1, 3]
title3 = 'CatBoostClassifier surface'
decision_boundary_plot(X1, y1, X1_train, y1_train, cb_clf, feature_indexes, title3)


cb_clf accuracy: 0.6851851851851852
[5 0 1 4 1 1 0 1 1 1 0 0 1 1 1 5 2 1 2 2 1 0 5 1 0 0 5 0 1 1 0 0 1 0 0 0 0
 0 0 5 1 5 1 0 1 1 0 1 0 1 0 1 5 0]

CatBoostRegressor

cb_reg = CatBoostRegressor(random_seed=0, logging_level='Silent')
cb_reg.fit(X2_train, y2_train)
cb_reg_pred_res = cb_reg.predict(X2_test)
cb_reg_mape = mean_absolute_percentage_error(cb_reg_pred_res, y2_test)
print(f'cb_reg mape: {cb_reg_mape}')
print(cb_reg_pred_res)


cb_reg mape: 0.3260573594870776
[268.21698587 226.61112865 152.56164473 105.39534082 185.56084388
 231.13386917 112.94031582 246.11217136 121.83631454 238.66069067
 193.92810529 171.53207065 120.95427566  98.87431921 301.0159263
  97.989809   170.68360243  70.03044356 104.9534818  235.1624283
 174.7895105  131.39173163 178.28683674 128.13631321 230.60611298
 186.37090017 131.52230822  61.453026   231.95028492 148.67901568
 186.2317954   80.45908918 137.68617262 171.24445717 128.77648933
 178.31364898 179.17236177 149.82094832 102.25676058 209.48231728
 116.01443961 169.06621701 110.9047463  210.24240477 158.28102362
  72.4532758  135.86931928 121.14865532  76.8103627  278.66222581
 127.85077736  55.25704176 144.51194393 170.06468442 271.51905928
 187.61879537 159.56680649 118.65520621 121.92004997 183.56316238
 248.87847858 137.77180529 117.98743897  82.53109543 255.59388802
 151.23062005  94.00606836 257.15481144 227.21705762  96.77322241
  78.34198817 118.09701594  91.2069645   91.70192792 125.65538331
 155.68222799 129.63411563 230.46496307 292.38275237 213.68057983
 131.76653094 217.93105223  50.37188156 256.16334997  94.4107044
  90.95547399 139.58356594 187.26517    127.97009716 171.85831366
  89.65051176  95.93129442  60.14437246 178.27466698 101.36657382
 106.15753799 206.11327567 217.74079838 130.83283251 138.63144499
 154.18156801 123.38315127 197.65233246 125.95249034 239.25024631
 139.69849648 245.02582928 288.17892899 122.76437963  70.023686
 233.36946028]

Преимущества и недостатки CatBoost

Преимущества:

высокая точность и скорость обучения в большинстве случаев;
возможность работы с категориальными признаками;
большое количество гиперпараметров для настройки алгоритма;
применяется для многих задач.

Недостатки:

нестабильная работа с несбалансированными данными;
сложность в конфигурации из-за большого количества гиперпараметров;
плохая документация (личное мнение).

Дополнительные источники

Статья «CatBoost: unbiased boosting with categorical features», Liudmila Prokhorenkova, Gleb Gusev, Aleksandr Vorobev, Anna Veronika Dorogush, Andrey Gulin.

Документация.

Лекция.

Пошаговое построение CatBoost (в ordered target encoding есть ошибки):

один;
два.

Особенности LightGBM

LightGBM (Light Gradient Boosting Machine) — реализация градиентного бустинга от компании Microsoft, способная обрабатывать большие наборы данных и при этом обеспечивать высокую точность. Рассмотрим более подробно ключевые особенности, которые на это повлияли.

Gradient-based One-Side Sampling (GOSS)

В отличие от классического градиентного бустинга, где регрессионные деревья обучаются на всём множестве X_train, в LightGBM деревья обучаются на подмножестве данных, полученном с помощью одностороннего отбора на основе градиента (GOSS), суть которого заключается в сортировке и выборе образцов top N с наибольшим градиентом — это означает, что именно этим данным следует уделить особое внимание, поскольку на них дерево будет ошибаться больше всего. Помимо этого, случайным образом производится отбор части образцов с низким градиентом с последующим присвоением им весов $\frac{1-a}{b}$ , чтобы избежать изменений в распределении данных. В данном случае — доля образцов top N в процентах с наибольшим градиентом, — доля образцов в процентах с низким градиентом.

Проще говоря, использование GOSS позволяет значительно ускорить обучение каждого последующего дерева в ансамбле путём уменьшения обучающего набора данных без особой потери в качестве прогнозов в большинстве случаев.

Histogram-based tree node splitting

При поиске наилучшего критерия разбиения узла в LightGBM также можно использовать гистограмму значений признаков: перебираются все пороговые значения гистограммы вместо всех значений признаков, что позволяет существенно ускорить поиск наилучшего критерия. Например, для признака "рост" можно использовать вопросы "рост" ⩽ 160, "рост" ⩽ 170 вместо "рост" ⩽ 163, "рост" ⩽ 167 и так далее. Как можно было заметить, гистограммы применяются в том или ином виде во всех трёх модификациях градиентного бустинга.

Exclusive Feature Bundling (EFB)

Предположим, что тем или иным образом в датасете имеются закодированные категориальные признаки, большинство из которых являются взаимоисключающими (те, которые одновременно не принимают ненулевые значения). При большом числе таких признаков обучение модели может занять слишком много времени и для решения данной проблемы в LightGBM применяется понижение размерности пространства признаков путём объединения взаимоисключающих признаков (EFB).

Стоит отметить, что в действительности строго взаимоисключающие признаки в данных встречаются крайне редко. Поэтому вводится такое понятие как доля конфликтов между признаками — отношение наблюдений от общего числа, где два признака принимают одновременно ненулевые значения.

Допустим, имеется датасет с признаками F0−F4 . В первую очередь стоит установить допустимую долю конфликтов, например, 25%. Тогда в случае из 8 образцов допустимое число конфликтов будет составлять 2. Далее строится матрица конфликтов между всеми признаками и производится подсчёт общей суммы конфликтов для каждого признака, после чего происходит их сортировка в порядке убывания.

На основе матрицы конфликтов строится взвешенный граф, у которого в полученном порядке отсекаются все рёбра с числом конфликтов, превышающим допустимое значение.

Работа Exclusive Feature Bundling с нуля на простом примере

Первой связкой будет F_0−F_1 . Не смотря на то что F_1−F_2 и F_1−F_3 не конфликтуют, их объединение невозможно из-за конфликтов F_0−F_2 и F_0−F_3 . Следующей связкой будет F_2−F_4 . Не смотря на то, что F_4 и F_3 не конфликтуют, их объединение невозможно из-за конфликта F_2−F_3 . Последним остаётся признак F_3 .

Новая связка будет состоять из ненулевых значений первого признака и ненулевых значений второго плюс смещение, равное максимальному значению первого признака: смещение каждого следующего признака будет равно сумме максимальных значений предыдущих. В случаях, когда наблюдается конфликт, берётся значение последнего признака со смещением.

Подробные расчёты приведены ниже.

Нетрудно заметить, что алгоритм EFB можно оптимизировать, игнорируя вычисления для всех нулевых значений в признаках. Также данную оптимизацию можно применить к histogram-based tree node splitting, что в целом снизит сложность построения гистограммы с O(data) до O(non-zero data).

Leaf-wise tree growth

Вместо построения деревьев слой за слоем, в LightGBM деревья строятся в глубину: рост продолжается в листовом узле с наибольшим информационным приростом, в результате чего дерево получается глубоким и несимметричным. Чаще всего такой подход превосходит симметричные деревья в плане точности.

Обучение на GPU

При работе с большими датасетами в LightGBM поддерживается обучение не только на GPU, но и распределённое обучение сразу на нескольких машинах.

На данный момент существуют следующие подходы:

Data parallel (образцы датасета разбиваются на локальные гистограммы, каждая из которых обрабатывается отдельно);
Feature parallel (признаки датасета разбиваются на локальные гистограммы, каждая из которых обрабатывается отдельно);
Voting parallel (на каждом процессе локально выбирается K лучших признаков для разбиения, после чего выбирается наилучший из них глобально).

Пакетная реализация LightGBM и оценка полученных результатов

Как можно заметить, в случае классификации LightGBM показал результат из коробки значительно лучше, чем предыдущие модификации бустинга. Также стоит отметить, что из всех трёх рассмотренных модификацией градиентного бустинга LightGBM является самой быстрой: чем больше датасет, тем сильнее будет заметна разница в плане скорости.

Полученные результаты приведены ниже.

LGBMClassifier

from lightgbm import LGBMClassifier, LGBMRegressor

lgb_clf = LGBMClassifier(random_state=0, verbose=-1)
lgb_clf.fit(X1_train, y1_train)
lgb_clf_pred_res = lgb_clf.predict(X1_test)
lgb_clf_accuracy = accuracy_score(lgb_clf_pred_res, y1_test)
print(f'lgb_clf accuracy: {lgb_clf_accuracy}')
print(lgb_clf_pred_res)

feature_indexes = [1, 3]
title4 = 'LGBMClassifier surface'
decision_boundary_plot(X1, y1, X1_train, y1_train, lgb_clf, feature_indexes, title4)


lgb_clf accuracy: 0.7407407407407407
[5 0 1 4 1 1 0 1 1 1 0 0 0 1 1 5 2 1 2 2 3 1 5 5 0 0 5 0 1 1 0 0 1 0 0 0 0
 0 0 5 1 4 1 0 0 1 0 1 0 1 0 1 5 0]

LGBMRegressor

lgb_reg = LGBMRegressor(random_state=0, verbose=-1)
lgb_reg.fit(X2_train, y2_train)
lgb_reg_pred_res = lgb_reg.predict(X2_test)
lgb_reg_mape = mean_absolute_percentage_error(lgb_reg_pred_res, y2_test)
print(f'lgb_reg_mape: {lgb_reg_mape}')
print(lgb_reg_pred_res)


lgb_reg_mape: 0.349719771087187
[261.46864967 223.24674049 179.60231224 104.76984808 197.67529058
 264.26116883 111.11355079 243.72059654 144.18045853 239.08131542
 199.90841705 170.37417433 151.67933516  89.30779664 297.93561211
  96.58862229 162.53285879  70.06113305 108.36436227 234.16276627
 207.7552967  136.83913826 172.38724529 110.26981866 228.1574526
 163.56817258 108.94516511  73.93303203 233.31869769 116.00042252
 195.39846082  72.54403358 164.38943926 194.42418913 130.42154381
 183.04435501 173.56352142 147.00774306  89.07365731 175.25759644
 108.72749406 144.48000593  99.60713604 196.86889512 160.47835096
  60.17798032 133.4909559  115.46543242  64.48286456 251.20520649
 135.52608509  45.16396653 161.70420785 187.28406745 274.21158331
 179.30355071 150.1563969  111.1275583  100.5067047  133.7868607
 269.98464504 159.03980859 118.01578638  75.41625416 249.0569831
 133.99026562 111.43954756 221.81954307 206.02676942  81.56098377
  72.5920367  101.31664062  93.31261471 111.24487763 149.40048547
 177.37205369 130.08118649 212.0573     294.138509   232.24330644
 109.5457663  181.3487432   63.20386576 261.47508264  88.43007908
  99.59568927 127.97978786 211.77672798 121.44351586 138.27282283
 121.01455597  91.26965383  68.92870597 156.03234199 101.80734511
 108.60244399 214.13968395 218.58499151 131.09438025 114.99269899
 187.63688894 117.5399017  165.85959666 110.74981366 238.97897095
 114.01806217 240.07138204 283.0195311  108.08395213  67.44250127
 238.97271264]

Преимущества и недостатки LightGBM

Преимущества:

высокая точность прогнозов и особенно скорость обучения;
возможность работы с категориальными признаками;
большое количество гиперпараметров для настройки алгоритма;
применяется для многих задач.

Недостатки:

возможна нестабильная работа на датасетах небольшого размера;
сложность в конфигурации из-за большого количества гиперпараметров.

Дополнительные источники

Статья «LightGBM: A Highly Efficient Gradient Boosting Decision Tree», Guolin Ke, Qi Meng, Thomas Finley, Taifeng Wang, Wei Chen, Weidong Ma, Qiwei Ye, Tie-Yan Liu.

Документация.

Лекции:

Какой бустинг лучше

Однозначного ответа на вопрос какой бустинг лучше нет. Если раньше можно было сказать, что при работе с категориальными признаками лучше использовать CatBoost, когда важна скорость — LightGBM, ну или XGBoost, если хочется стабильное решение и нет времени на эксперименты, то сейчас такое утверждение будет неверным: как можно было заметить, все три модификации успели скопировать друг у друга много хороших идей, но исторически они отличались довольно сильно.

Более правильным будет утверждение, что выбор наилучшего бустинга будет зависеть от конкретной задачи и данных, которые применяются для обучения модели: в разных сценариях одни и те же алгоритмы могут показывать как лучшие результаты в плане скорости и точности, так и наоборот — худшие. Таким образом, выбор наиболее оптимального бустинга будет заключаться в проведении экспериментов с разными модификациями и сравнении полученных результатов.

Несколько полезных источников со сравнением бустингов: один, два, три.

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13 мар. 2024 г.

12.11.25 09:37 patricialovick86

How To Recover Your Bitcoin Without Falling Victim To Scams: A Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected] You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1
13.11.25 19:01 peggy09

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
13.11.25 20:05 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
13.11.25 20:05 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
13.11.25 22:51 ashley11

Recover All Lost Cryptocurrency From Scammers
13.11.25 22:52 ashley11

Recover All Lost Cryptocurrency From Scammers TREQORA INTEL has exhibited unparalleled strength in the realm of recovery. They stand out as the premier team to collaborate with if you encounter withdrawal difficulties from the platform where you’ve invested. Recently, I engaged with them to recover over a million dollars trapped in an investment platform I’d been involved with for months. I furnished their team with every detail of the investment via Email (SUPPORT @ TREQORA . C O M”), including accounts, names, and wallet addresses to which I sent the funds. This decision proved to be the best I’ve made, especially after realizing I had been sc**med by the company. Initially, I harbored doubts about their services, but I was proven wrong. TREQORA INTEL ensures exemplary service delivery and ensures the perpetrators face justice. They employ advanced techniques to ensure you regain access to your funds. Understandably, many individuals who have fallen victim to investment scams may still harbor trepidation about engaging in online services again due to the trauma of being sc**med. However, I implore you to take action. Seek assistance from TREQORA INTEL today and witness their remarkable capabilities firsthand. Among the myriad of hackers available, TREQORA INTEL stands head and shoulders above the rest. While I may not have sampled all of them, the few I attempted to work with previously were unhelpful and solely focused on depleting the little funds I had left. I am grateful that I resisted their enticements, and despite the time it took me to discover TREQORA INTEL, they ultimately fulfilled my primary objective. I am confident they will execute the task proficiently. Without their intervention, I would have remained despondent and perplexed indefinitely. Don’t make the error of entrusting sc**mers to rectify a sc*m; the consequences are evident. Email:support@treqora. com,WhatsApp: ‪‪‪‪‪‪+1 (7 7 3) 9 7 7 - 7 8 7 7‬‬‬‬ ‬‬,Website: Treqora. com. How Can I Recover My Lost Bitcoin From A Romance Scammer-HIRE TREQORA INTEL
13.11.25 23:36 daisy

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
14.11.25 03:42 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.11.25 03:42 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
14.11.25 08:38 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
14.11.25 10:39 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
14.11.25 12:12 daisy

i Lost $200,000 to a phishing scam in 2022. Funds went to a mixer service. Davies traced 70% through Ethereum layers. He teamed with an exchange to freeze the rest. i got $140,000 back in six months. Hiring Davies means clear steps. You share details. He checks facts. Then, the hunt begins. Expect ups and downs, but his plan keeps it steady. you can reach out to him by sending an email to anthonydaviestech {@} gmail com
14.11.25 15:07 caridad

Perth Family Saved After $400K Crypto Scam Our family in Perth, WA invested through what we thought was a trusted platform but ended up being a fraudulent investment scheme. We lost nearly AUD 420,000 worth of BTC and USDT. Luckily, a friend recommended Bitreclaim.com. Their 24/7 customer support assigned us a smart contract audit specialist who asked for wallet addresses and transaction hashes. With their forensic blockchain trace, they recovered over 5.1 BTC directly into our hardware wallet. For Perth investors: don’t give up hope. Submit a case at Bitreclaim.com immediately. Their professionalism and success rate in Australia is unmatched.
14.11.25 18:33 justinekelly45

FAST & RELIABLE CRYPTO RECOVERY SERVICES Hire iFORCE HACKER RECOVERY I was one of many victims deceived by fake cryptocurrency investment offers on Telegram. Hoping to build a retirement fund, I invested heavily and ended up losing about $470,000, including borrowed money. Just when I thought recovery was impossible, I found iForce Hacker Recovery. Their team of crypto recovery experts worked tirelessly and helped me recover my assets within 72 hours, even tracing the scammers involved. I’m deeply thankful for their professionalism and highly recommend their services to anyone facing a similar situation. Website: ht tps://iforcehackers. co m WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om
14.11.25 20:56 juliamarvin

Firstly, the importance of verifying the authenticity of online communications, especially those about financial matters. Secondly, the potential for recovery exists even in cases where it seems hopeless, thanks to innovative services like TechY Force Cyber Retrieval. Lastly, the cryptocurrency community needs to be more aware of these risks and the available solutions to combat them. My experience serves as a warning to others to be cautious of online impersonators and never to underestimate the potential for recovery in the face of theft. It also highlights the critical role that professional retrieval services can play in securing your digital assets. In conclusion, while the cryptocurrency space offers unparalleled opportunities, it also presents unique challenges, and being informed and vigilant is key to navigating this landscape safely. W.h.a.t.s.A.p.p.. +.15.6.1.7.2.6.3.6.9.7. M.a.i.l T.e.c.h.y.f.o.r.c.e.c.y.b.e.r.r.e.t.r.i.e.v.a.l.@.c.o.n.s.u.l.t.a.n.t.c.o.m. T.e.l.e.g.r.a.m +.15.6.1.7.2.6.3.6.9.7
15.11.25 12:47 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 14:39 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.11.25 14:39 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
15.11.25 15:31 MATT PHILLIP

I never imagined I’d fall for a crypto romance scam but it happened. Over the course of a few months, I sent nearly $184,000 worth of Bitcoin to someone I genuinely believed I was building a future with. When they disappeared without a trace, I was left heartbroken, humiliated, and financially devastated. For a long time, I didn’t tell anyone. I felt ashamed. But eventually, while searching for answers, I came across a Reddit thread that mentioned Agent Jasmine Lopez a crypto recovery agent. I reached out, not expecting much. To my surprise, she treated me with kindness, not judgment. She used advanced tools like blockchain forensics, IP tracing, and smart contract analysis and with persistence and legal support, she was able to recover nearly 85% of what I lost. I know not everyone gets that kind of outcome, but thanks to [email protected] WhatsApp at +44 736-644-5035, I’ve started to reclaim not just my assets, but my confidence and peace of mind. If you’re going through something similar, you’re not alone and there is hope.
15.11.25 15:52 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
16.11.25 14:43 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.11.25 14:44 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
16.11.25 20:38 [email protected]

A scam cost me $72,000 in USDT. It shook me up. USDT is a stablecoin linked to the dollar. Its value stays even. I believed I found a safe path to build my wealth. At the start, all seemed fine. My account grew to $120,000 in profits. But when I tried to withdraw, the site locked me out. No way to get in. No money left. Fear took over. I felt stuck and alone. These frauds hit crypto investors often. They lure with fast riches. Then they steal your cash and disappear. Billions vanish each year from such schemes. I looked for aid in every spot. Online boards. Help chats. None helped. Then a buddy offered support. He had dealt with the same issue once. He mentioned Sylvester Bryant. My friend praised his expertise. I contacted him at once. His email is [email protected]. Sylvester Bryant changed everything. He heard my tale with no blame. His crew jumped in quickly. They checked all scam details first. One by one, they followed my lost USDT trail. They used software to track the blockchain. That is the open log of coin transfers. It reveals fund paths. Scammers try to cover their steps. Bryant's team went far. They reached out to related platforms and services. Each day brought progress. No easy ways. They shared updates with me always. Each message and talk stayed open and true. Finally, they got back every dollar. My $52,000 returned whole. The effort needed drive and resolve. Bryant's fairness shone through. He added no secret costs. Only fair pay for the job. My worry faded. I relaxed once more. Nights grew calm. My faith in recovery grew strong. If fraud stole your funds, move fast. Contact Sylvester Bryant. He treats such cases with skill. Email at [email protected]. Or use WhatsApp at +1 512 577 7957 or +44 7428 662701. Do not delay. Reclaim what is yours.
17.11.25 03:24 johnny231

INFO@THEBARRYCYBERINVESTIGATIONSDOTCOM is one of the best cyber hackers that i have actually met and had an encounter with, i was suspecting my partner was cheating on me for some time now but i was not sure of my assumptions so i had to contact BARRY CYBER INVESTIGATIONS to help me out with my suspicion. During the cause of their investigation they intercepted his text messages, social media(facebook, twittwer, snapchat whatsapp, instagram),also call logs as well as pictures and videos(deleted files also) they found out my spouse was cheating on me for over 3 years and was already even sending nudes out as well as money to anonymous wallets,so i deciced to file for a divorce and then when i did that i came to the understanding that most of the cryptocurrency we had invested in forex by him was already gone. BARRY CYBER INVESTIGATIONS helped me out through out the cause of my divorce with my spouse they also helped me in retrieving some of the cryptocurrency back, as if that was not enough i decided to introduce them to another of my friend who had lost her most of her savings on a bad crytpo investment and as a result of that it affected her credit score, BARRY CYBER INVESTIGATIONS helped her recover some of the funds back and helped her build her credit score, i have never seen anything like this in my life and to top it off they are very professional and they have intergrity to it you can contact them also on their whatsapp +1814-488-3301. for any hacking or pi jobs you can contact them and i assure you nothing but the best out of the job
17.11.25 11:26 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
17.11.25 11:27 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.11.25 01:56 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I got connected to the best female expert AGENT Jasmine Lopez,,( [email protected] ) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
19.11.25 08:11 JuneWatkins

I’m June Watkins from California. I never thought I’d lose my life savings in Bitcoin. One wrong click, a fake wallet update, and $187,000 vanished in seconds. I cried for days, felt stupid, ashamed, and completely hopeless. But God wouldn’t let me stay silent or defeated. A friend sent me a simple message: “Contact Mbcoin Recovery Group, they specialize in this.” I was skeptical (there are so many scammers), but something in my spirit said “try.” I reached out to Mbcoin Recovery Group through their official site and within minutes their team responded with kindness and clarity. They walked with me step by step, and stayed in constant contact. Three days later, I watched in tears as every single Bitcoin returned to my wallet, 100% recovered. God turned my mess into a message and my shame into a testimony! If you’ve lost crypto and feel it’s gone forever, don’t give up. I’m living proof that recovery is possible. Thank you, Mbcoin Recovery Group, and thank You, Jesus, for never leaving me stranded. contact: (https://mbcoinrecoverygrou.wixsite.com/mb-coin-recovery) (Email: [email protected]) (Call Number: +1 346 954-1564)
19.11.25 08:26 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) (Email [email protected])
19.11.25 08:27 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
19.11.25 16:30 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.11.25 16:30 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
20.11.25 15:55 mariotuttle94

HIRE THE BEST HACKER ONLINE FOR CRYPTO BITCOIN SCAM RECOVERY / iFORCE HACKER RECOVERY After a security breach, my husband lost $133,000 in Bitcoin. We sought help from a professional cybersecurity team iForce Hacker Recovery they guided us through each step of the recovery process. Their expertise allowed them to trace the compromised funds and help us understand how the breach occurred. The experience brought us clarity, restored a sense of stability, and reminded us of the importance of strong digital asset and security practices. Website: ht tps:/ /iforcehackers. c om WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om
21.11.25 10:56 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
21.11.25 10:56 marcushenderson624

Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.11.25 04:41 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I got connected to the best female expert AGENT Jasmine Lopez,,( [email protected] ) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
22.11.25 22:04 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.11.25 22:04 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
22.11.25 22:05 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.11.25 03:34 Matt Kegan

SolidBlock Forensics are absolutely the best Crypto forensics team, they're swift to action and accurate
23.11.25 09:54 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
23.11.25 18:01 mosbygerry

I recently had the opportunity to work with a skilled programmer who specialized in recovering crypto assets, and the results were nothing short of impressive. The experience not only helped me regain control of my investments but also provided valuable insight into the intricacies of cryptocurrency technology and cybersecurity. The journey began when I attempted to withdraw $183,000 from an investment firm, only to encounter a series of challenges that made it impossible for me to access my funds. Despite seeking assistance from individuals claiming to be Bitcoin miners, I was unable to recover my investments. The situation was further complicated by the fact that all my deposits were made using various cryptocurrencies that are difficult to trace. However, I persisted in my pursuit of recovery, driven by the determination to reclaim my losses. It was during this time that I discovered TechY Force Cyber Retrieval, a team of experts with a proven track record of successfully recovering crypto assets. With their assistance, I was finally able to recover my investments, and in doing so, gained a deeper understanding of the complex mechanisms that underpin cryptocurrency transactions. The experience taught me that with the right expertise and guidance, even the most seemingly insurmountable challenges can be overcome. I feel a sense of obligation to share my positive experience with others who may have fallen victim to cryptocurrency scams or are struggling to recover their investments. If you find yourself in a similar situation, I highly recommend seeking the assistance of a trustworthy and skilled programmer, such as those at TechY Force Cyber Retrieval. WhatsApp (+1561726 3697) or (+1561726 3697). Their expertise and dedication to helping individuals recover their crypto assets are truly commendable, and I have no hesitation in endorsing their services to anyone in need. By sharing my story, I hope to provide a beacon of hope for those who may have lost faith in their ability to recover their investments and to emphasize the importance of seeking professional help when navigating the complex world of cryptocurrency.
24.11.25 11:43 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.11.25 11:43 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
24.11.25 16:34 Mundo

I wired 120k in crypto to the wrong wallet. One dumb slip-up, and poof gone. That hit me hard. Lost everything I had built up. Crypto moves on the blockchain. It's like a public record book. Once you send, that's it. No take-backs. Banks can fix wire mistakes. Not here. Transfers stick forever. a buddy tipped me off right away. Meet Sylvester Bryant. Guy's a pro at pulling back lost crypto. Handles cases others can't touch, he spots scammer moves cold. Follows money down secret paths. Mixers. Fake trades. Hidden swaps. You name it, he tracks it. this happens to tons of folks. Fat-finger a key. Miss one digit in the address. Boom. Billions vanish like that each year. I panicked. Figured my stash was toast for good. Bryant flipped the script. He jumps on hard jobs quick. Digs deep. Cracks the trail. Got my funds back safe. You're in the same boat? Don't sit there. Hit him up today. Email [email protected]. WhatsApp +1 512 577 7957. Or +44 7428 662701. Time's your enemy here. Scammers spend fast. Chains churn non-stop. Move now. Grab your cash back home.
25.11.25 05:15 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
25.11.25 13:31 mickaelroques52

CRYPTO TRACING AND INVESTIGATION EXPERT: HOW TO RECOVER STOLEN CRYPTO_HIRE RAPID DIGITAL RECOVERY
25.11.25 13:31 mickaelroques52

I’ve always considered myself a careful person when it comes to money, but even the most cautious people can be fooled. A few months ago, I invested some of my Bitcoin into what I believed was a legitimate platform. Everything seemed right, professional website, live chat support and even convincing testimonials. I thought I had done my homework. But when I tried to withdraw my funds, everything fell apart. My account was blocked, the so-called support team disappeared and I realized I had been scammed. The shock was overwhelming. I couldn’t believe I had fallen for it. That Bitcoin represented years of savings and sacrifices and it felt like everything had been stolen from me in seconds. I didn’t sleep for days and I was angry at myself for trusting the wrong people. In my desperation, I started searching for solutions and came across Rapid Digital Recovery. At first, I thought it was just another promise that would lead nowhere. But after speaking with them, I realized this was different. They were professional, clear and understanding. They explained exactly how they track stolen funds through blockchain forensics and what steps would be taken in my case. I gave them all the transaction details and they immediately got to work. What impressed me most was their transparency, they gave me updates regularly and kept me involved in the process. After weeks of investigation, they achieved what I thought was impossible: they recovered my stolen Bitcoin and safely returned it to my wallet. The relief I felt that day is indescribable. I went from feeling hopeless and broken to feeling like I had been given a second chance. I am forever grateful to Rapid Digital Recovery. They didn’t just recover my money, they restored my peace of mind. If you’re reading this because you’ve been scammed, please know you’re not alone and that recovery is possible. I’m living proof that with the right help, you can get your funds back... Contact Info Below WhatSapp: + 1 414 807 1485 Email: rapiddigitalrecovery (@) execs. com Telegram: + 1 680 5881 631
26.11.25 18:18 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.11.25 18:20 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
26.11.25 19:13 James Robert

I am James Robert from Chicago. Few months ago, I fell victim to an online Bitcoin investment scheme that promised high returns within a short period. At first, everything seemed legitimate, their website looked professional, and the people behind it were very convincing. I invested a significant amount of money about $440,000 with the way they talk to me into investing on their bitcoin platform. Two months later I realized that it was a scam when I could no longer have access to my account and couldn’t withdraw my money. At first, I lost hope that I wouldn't be able to get my money back, I cried and was angry at how I even fell victim to a scam. For days after doing some research and seeking professional help online, I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how they have helped people recover their money back from scammers. I reported the case immediately to them and gather every transaction detail, documentation and sent it to them. Today, I’m very happy because the GREAT WHIP RECOVERY CYBER SERVICES help me recover all my money I was scammed. You can contact GREAT WHIP RECOVERY CYBER SERVICES if you have ever fallen victim to scam. Email: [email protected] or Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site
27.11.25 10:56 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 10:56 harristhomas7376

"In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 20:04 deborah113

Scammed Crypto Asset Recovery Solution Hire iFORCE HACKER RECOVERY When I traded online, I lost both my investment money and the anticipated gains. Before permitting any withdrawals, the site kept requesting more money, and soon I recognized I had been duped. It was really hard to deal with the loss after their customer service ceased responding. I saw a Facebook testimonial about how iForce Hacker Recovery assisted a victim of fraud in getting back the bitcoin she had transferred to con artists. I contacted iForce Hacker Recovery, submitted all relevant case paperwork, and meticulously followed the guidelines. I'm relieved that I was eventually able to get my money back, including the gains that were initially displayed on my account. I'm sharing my story to let others who have been conned know that you can recover your money. WhatsApp: +1 240-803-3706 Email: iforcehk @ consultant. c om Website: ht tps:/ /iforcehackers. c om
27.11.25 23:48 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
27.11.25 23:48 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.11.25 00:08 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I found someone Agent Jasmine Lopez ([email protected])WhatsApp at +44 736-644-5035. ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it.
28.11.25 11:15 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.11.25 11:15 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
28.11.25 11:43 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
28.11.25 11:43 elizabethmadison

My name is Elizabeth Madison currently living in New York. There was a time I felt completely broken. I had trusted a fraudulent bitcoin investment organization, who turned out to be a fraudster. I sent money, believing their sweet words and promises on the interest rate I will get back in return, only to realize later that I’ve been scammed. On the day of withdrawal there was no money in my account. The pain hit deep. I couldn’t sleep, I kept asking myself how I could have been so careless, meanwhile my mom was battling with a stroke and the expenses were too much. For days, I cried and blamed myself. The betrayal, the disappointment and my mom's health issues all of this stress made me want to give up on life. But one day, I decided that sitting in pain wouldn’t solve anything. I picked myself up and chose to fight for what I lost then I came across GREAT WHIP RECOVERY CYBER SERVICES and saw how he helped people recover their funds from online fraud. I emailed all the transactions and paperwork I had with the fraudulent organization and they helped me recover all my lost money in just five days. If you have ever fallen victim to scammers, contact GREAT WHIP RECOVERY CYBER SERVICES to help you recover every penny you have lost. (Text +1(406)2729101) Website https://greatwhiprecoveryc.wixsite.com/greatwhip-site (Email [email protected])
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
29.11.25 12:35 elizabethrush89

God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1
30.11.25 20:37 robertalfred175

CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.12.25 12:27 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
01.12.25 12:27 Thomas Muller

YOU CAN REACH OUT TO GREAT WHIP RECOVERY CYBER SERVICES FOR HELP TO RECOVER YOUR STOLEN BTC OR ETH BACK WHATSAPP +1(208)713-0697 I once fell victim to online investment scheme that cost me a devastating €254,000. I’m Thomas Muller from Berlin, Germany. The person I trusted turned out to be a fraud, and the moment I realized I’d been deceived, my entire world stopped. I immediately began searching for legitimate ways to recover my funds and hold the scammer accountable. During my search, I came across several testimonies of how Great Whip Recovery Cyber Services helped some people recover money they lost to cyber fraud, I contacted Great Whip Recovery Cyber Service team and provided all the evidence I had. Within about 36 hours, the experts traced the digital trail left by the fraudster, the individual was eventually tracked down and I recovered all my money back. You can contact them with, website https://greatwhiprecoveryc.wixsite.com/greatwhip-site text +1(406)2729101 email [email protected]
01.12.25 23:45 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
01.12.25 23:45 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
02.12.25 02:21 donald121

In 2025 alone, hackers stole over $1.5 billion in digital assets from users worldwide. That's a wake-up call for anyone holding crypto. Theft hits hard because once funds move, they're tough to get back. Common ways it happens include phishing emails that trick you into giving up keys, big exchange breaches, or malware sneaking into your wallet. Marie guide walks you through steps to recover stolen cryptocurrency. You'll learn quick actions to stop more loss, how to trace funds, and ways to fight back legally. Plus, tips to avoid this mess next time. reach her (infocyberrecoveryinc@gmail com and whatsapp:+1 7127594675)
02.12.25 15:05 Matt Kegan

Reach out to SolidBlock Forensics if you want to get back your coins from fake crypto investment or your wallet was compromised and all your coins gone. SolidBlock Forensics provide deep ethical analysis and investigation that enables them to trace these schemes, and recover all your funds. Their services are professional and reliable.
03.12.25 09:22 tyrelldavis1

I still recall the day I fell victim to an online scam, losing a substantial amount of money to a cunning fraudster. The feeling of helplessness and despair that followed was overwhelming, and I thought I had lost all hope of ever recovering my stolen funds. However, after months of searching for a solution, I stumbled upon a beacon of hope - GRAYWARE TECH SERVICE, a highly reputable and exceptionally skilled investigative and recovery firm. Their team of expert cybersecurity professionals specializes in tracking and retrieving money lost to internet fraud, and I was impressed by their unwavering dedication to helping victims like me. With their extensive knowledge and cutting-edge technology, they were able to navigate the complex world of online finance and identify the culprits behind my loss. What struck me most about GRAYWARE TECH SERVICE was their unparalleled expertise and exceptional customer service. They took the time to understand my situation, provided me with regular updates, and kept me informed throughout the entire recovery process. Their transparency and professionalism were truly reassuring, and I felt confident that I had finally found a reliable partner to help me recover my stolen money. Thanks to GRAYWARE TECH SERVICE, I was able to recover a significant portion of my lost funds, and I am forever grateful for their assistance. Their success in retrieving my money not only restored my financial stability but also restored my faith in the ability of authorities to combat online fraud. If you have fallen victim to internet scams, I highly recommend reaching out to GRAYWARE TECH SERVICE - their expertise and dedication to recovering stolen funds are unparalleled, and they may be your only hope for retrieving what is rightfully yours. You can reach them on whatsapp+18582759508 web at ( https://graywaretechservice.com/ ) also on Mail: ([email protected]
03.12.25 21:01 VERONICAFREDDIE809

Earlier this year, I made a mistake that changed everything. I downloaded what I thought was a legitimate trading app I’d found through a Telegram channel. At first, everything looked real until I tried to withdraw. My entire investment vanished into a bot account, and that’s when the truth hit me: I had been scammed. I can’t describe the feeling. It was as if the ground dropped out from under me. I blamed myself. I felt stupid, ashamed, helpless every painful emotion at once. For a while, I couldn’t even talk about it. I thought no one would understand. But then I found someone Agent Jasmine Lopez ([email protected]) ,She didn’t brush me off or judge me. She took my fear seriously. She followed leads I didn’t even know existed, and identified multiple off-chain indicators and wallet clusters linked to the scammer network, she helped me understand what had truly happened behind the scenes. For the first time since everything fell apart, I felt hope. Hearing that other people students, parents, hardworking people had been targeted the same way made me realize I wasn’t alone. What happened to us wasn’t stupidity. It was a coordinated attack. We were prey in a system built to deceive. And somehow, through all the chaos, Agent Jasmine stepped in and shined a light into the darkest moment of my life. I’m still healing from the experience. It changed me. But it also reminded me that even when you think you’re at the end, sometimes a lifeline appears where you least expect it. Contact her at [email protected] WhatsApp at +44 736-644-5035.
03.12.25 22:17 Tonerdomark

I lost $300,000 in USDC to a phishing scam. Scammers tricked me with a fake wallet link. They drained my account fast. I felt hopeless. No way to get it back. Then Sylvester stepped in. His skills traced the funds. He recovered every bit. USDC is a stablecoin tied to the dollar. Phishing scams hit hard in crypto. They fool you with urgent emails or sites. Billions vanish each year this way. Sylvester knows blockchain tracks. He used tools to follow the trail. I got my money back in weeks. Skills like his turn loss to win. Don't wait if scammed. Contact Mr. Sylvester now. Email: yt7cracker@gmail. com. WhatsApp only: + 1 512 577 7957 or + 44 7428 662701. He helped me. He can help you.
04.12.25 01:37 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.12.25 01:37 michaeldavenport238

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
04.12.25 04:35 Tonerdomark

I lost $300,000 in USDC to a phishing scam. Scammers tricked me with a fake wallet link. They drained my account fast. I felt hopeless. No way to get it back. Then Sylvester stepped in. His skills traced the funds. He recovered every bit. USDC is a stablecoin tied to the dollar. Phishing scams hit hard in crypto. They fool you with urgent emails or sites. Billions vanish each year this way. Sylvester knows blockchain tracks. He used tools to follow the trail. I got my money back in weeks. Skills like his turn loss to win. Don't wait if scammed. Contact Mr. Sylvester now. Email: [email protected]. WhatsApp only: + 1 512 577 7957 or + 44 7428 662701. He helped me. He can help you.
04.12.25 10:32 Tonerdomark

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04.12.25 18:25 smithhazael

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04.12.25 21:45 elizabethrush89

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05.12.25 08:35 into11

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05.12.25 08:48 Tonerdomark

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06.12.25 01:44 Tonerdomark

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06.12.25 01:48 Tonerdomark

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06.12.25 10:36 Thomas Muller

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06.12.25 10:36 Thomas Muller

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06.12.25 10:39 michaeldavenport238

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06.12.25 10:42 michaeldavenport238

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07.12.25 08:43 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = [email protected]
08.12.25 02:17 liam

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08.12.25 09:07 Tonerdomark

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09.12.25 00:18 swanky

For a long time, I had heard tales of individuals striking it rich through cryptocurrency investments, but I had little knowledge of how the system operated. The potential for financial gain piqued my interest, and I decided to dive in and invest. To help me navigate this complex landscape, I joined a group of online traders who promised to guide me through the investment process. Their confidence and expertise made me feel reassured about my decision.After spending some time learning from them and observing their trading strategies, I felt compelled to invest a substantial amount of money to which i lost, now in search of recovering my funds i got referred to anthonydavies on telegram a funds recovery specialist with his team help i was able to get back $300000 of my usdc back. you can reach him via anthonydaviestech AT gmail dot com
09.12.25 01:01 Tonerdomark

SYLVESTER BRYANT WAS A PROFESSIONAL/ RELIABLE HACKER AND HIGHLY RECOMMENDED I’m very excited to speak about him as a Bitcoin Recovery agent, this cyber security company was able to assist me in recovering my stolen funds in cryptocurrency. I’m truly amazed by their excellent service and professional work. I never thought I could get back my funds until I approached them with my problems and provided all the necessary information. It took them time to recover my funds and I was amazed. Without any doubt, I highly recommend Sylvester for your BITCOIN, USDC, USDT, ETH Recovery, for all Cryptocurrency recovery, digital funds recovery, hacking Related issues, contact Sylvester Bryant professional services waapp only= +1 512 577 7957 or + 44 7428 662701 EMAIL = Yt7CRACKER@gmail. com
09.12.25 05:44 swanky

For a long time, I had heard tales of individuals striking it rich through cryptocurrency investments, but I had little knowledge of how the system operated. The potential for financial gain piqued my interest, and I decided to dive in and invest. To help me navigate this complex landscape, I joined a group of online traders who promised to guide me through the investment process. Their confidence and expertise made me feel reassured about my decision.After spending some time learning from them and observing their trading strategies, I felt compelled to invest a substantial amount of money to which i lost, now in search of recovering my funds i got referred to anthonydavies on telegram a funds recovery specialist with his team help i was able to get back $300000 of my usdc back. you can reach him via anthonydaviestech AT gmail dot com
09.12.25 10:24 lane3215

It is distressing to lose USDT to a bitcoin wallet hack. Although challenging, recovering stolen USDT is feasible. Your chances increase if you move swiftly and strategically. Marie can help you with reporting the theft, recovering USDT, and taking immediate action. You can reach her via mail at [email protected], WhatsApp at +1 7127594675.
09.12.25 10:25 lane3215

It is distressing to lose USDT to a bitcoin wallet hack. Although challenging, recovering stolen USDT is feasible. Your chances increase if you move swiftly and strategically. Marie can help you with reporting the theft, recovering USDT, and taking immediate action. You can reach her via mail at [email protected], WhatsApp at +1 7127594675.
09.12.25 14:16 Matt Kegan

Grateful i came across SolidBlock Forensics. After investing in crypto trade and couldn't make withdrawals, it dawned on me something was wrong. They kept on asking for taxes, fees for maintenance, and more money for admin reasons. But being represented by SolidBlock Forensics, i was able to file reports, and finally, received all my investments with returns. Its great to know we have professionals that handle such issues and get the job done.